1. Table of Contents Recall an important property of inverse functions: the composite of the functions is x. If we assume that functions f and g are inverses of each other, then... Since the exponential and logarithmic functions are inverses of each other, their composites result in x. Logarithmic and Exponential Functions - Inverses

2. Table of Contents Slide 2 Logarithmic and Exponential Functions - Inverses Let exponential and logarithmic functions be given by: Form the composite of f with g: Using the inverse property discussed earlier, this means... Note that for the exponential and the logarithm, the bases are the same real number b.

3. Table of Contents Slide 3 Logarithmic and Exponential Functions - Inverses Example 1: Simplify Since this is the composite of an exponential function and a logarithmic function, each with a base of 3, the result is...

4. Table of Contents Slide 4 Logarithmic and Exponential Functions - Inverses Example 2: Simplify

5. Table of Contents Slide 5 Logarithmic and Exponential Functions - Inverses Note the use of the inverse property in the next to last step where...

6. Table of Contents Slide 6 Logarithmic and Exponential Functions - Inverses Let exponential and logarithmic functions be given by: Now form the composite of g with f: Using the inverse property g(f(x)) = x, this means... Note that for the logarithm and the exponential, the bases are the same real number b.

7. Table of Contents Slide 7 Logarithmic and Exponential Functions - Inverses Example 3: Simplify Since this is the composite of a logarithmic function and an exponential function, each with a base of 4, the result is...

8. Table of Contents Slide 8 Logarithmic and Exponential Functions - Inverses Example 4: Simplify Note the use of the inverse property in the last step where...

9. Table of Contents Logarithmic and Exponential Functions - Inverses